Such devices, generally referred to as vertical or horizontal slides when mounted on automobile doors with fixed panes, usually consist of a standard section, with sealing lips of a relatively flexible elastomer or plastomer, and a part of relatively hard elastomer or plastomer, approximately semicircular or U-shaped, which enables mounting or assembly of the slide on the metal plates of the door or the body of the door on which it is mounted. Many embodiments of such slides have already been proposed to solve the twofold problem raised by the need to trim the door frame, while guaranteeing the sealing of the two faces of the mobile window pane's surface at its junction with said frame in which it is mounted without hindering its sliding, both for automobile windows and panes of the usual type, and of the flush-mounted or approximately flush-mounted type, as described in EP-0-308 377 or DE-3512973. In certain known embodiments, the slides are in two parts, so that, added to the drawbacks associated with the cost of management of a large number of spare parts, are those of the behavior and appearance after mounting, as well as those incurred by sealing defects, such as noise and/or the deterioration of exposed parts, owing to the difficulty of achieving a satisfactory junction of the two parts of the slide. Furthermore, the mounting of the known slides on the rabbet of the bay on which they are mounted is often relatively complex, and tends to prevent the esthetically pleasing appearance provided by the trim, typically black, extending about the periphery of the window bay and generally referred to as "styling black" or "noir de style".